The Japanese tech conglomerate’s plans to list its cash-generating telecoms unit have suffered a blow after a local rival slashed its mobile-phone rates

Softbank’s founder, Masayoshi Son, loves to talk about futuristic concepts that are more about machines than humans: artificial superintelligence, brain computers or self-driving cars. Right now, he has to deal with the messy politics of mere mortals.

Shares in the Japanese technology conglomerate dived 8.2% Thursday after Japan’s largest wireless carrier, NTT DoCoMo, said it would slash its mobile-phone rates by up to 40%, starting in April. DoCoMo’s move came after recent complaints from a high-level government official...